Class 9 Math for AI (Statistics & Probability) PDF

Ch-3 Math for AI (Statistics & Probability) Objectives: To appreciate the role of mathematics in Artificial Intelligence and Machine learning. to know the application side of mathematics and to have a basic level of understanding of the mathematical models. learn about th...

Ch-3 Math for AI (Statistics & Probability) Objectives: To appreciate the role of mathematics in Artificial Intelligence and Machine learning. to know the application side of mathematics and to have a basic level of understanding of the mathematical models. learn about the different ways data can be represented and summarized graphically. Learning outcomes: Students will be able to understand the importance of mathematics in the field of AI. Students will be able to identify the essential mathematical concepts Students will be able to define statistics and probability and describe their applications in AI Pre-requisites Basic mathematical knowledge and analytical ability Basic familiarity with AI Let us relate: Activity 1: ✓ How did you solve any puzzles? _______________________________________________________________ ✓ Was there any pattern that you recognized which could help you solve the puzzles? _______________________________________________________________ Activity 2: Find the missing number in the following series. 3,6,9,12,15,? 11,13,15,17,? 20,17,14,11,? Dear learners in the above series, you need to find out the missing number? Will you able to find the missing number without analysing or determining any pattern in the series to solve the puzzle? How Maths and AI is related? Math is all about exploring patterns and using them to understand the world around us. So, keep your eyes peeled for patterns, and unleash your inner math detective! What are Patterns? Patterns are recognizable arrangements of numbers, shapes, colors, or even sounds. They can be simple repetitions, like the stripes on a zebra, or more complex arrangements, like the Fibonacci sequence in nature (think spirals in sunflowers or seashells!). 1 Math, the Pattern Detective: Mathematicians are like detectives who love to crack the code of patterns. They use a variety of tools to: Identify Patterns: The first step is spotting the pattern itself. Is it a sequence of numbers that increases or decreases? Is it a geometric arrangement of shapes? Describe Patterns: Once identified, we can describe the pattern using rules or formulas. For example, the sequence 2, 4, 6, 8... follows the rule "add 2 each time." Predict Patterns: The magic of math allows us to predict what comes next in a pattern. This is super useful in areas like finance or weather forecasting. Why are Patterns Important in Math? Patterns are the building blocks of math. Understanding them helps us: Solve Problems: Many math problems involve recognizing Number Pattern Challenge: and using patterns to find solutions. For example, if you see a Create your own number pattern and pattern in a multiplication table, you can use it to solve similar challenge your friends to guess the rule. problems quickly. Can they continue the pattern and predict the next few numbers? Develop Thinking Skills: Looking for patterns helps us think logically, analyze information, and make connections between different ideas. Patterns are everywhere in nature, science, and even music! Understanding them helps us appreciate the beauty and order in the world. Understanding math will help us to better understand AI and its way of working, but what kind of math is needed for AI? Let us take a look! Essential Mathematics for AI Let’s think and answer the following questions: 1. 11, 22, 33, 44, 55 – Can you find out the middle value from the given numbers? ____________________________________________ Fig: AI Model identifying a dog. 2  2. In the given figure, which of the two lines is more slanted? Line 1 or Line 2? ________________________________________ 3. A has 2 plants, B has 3 plants, C has 1 plant, D has 7 plants. How many plants are there in total? _______________________________________ 4. If the coin shown in the figure below is used for a toss, what can be the possible result? _____________________ Just like us, AI can also solve 4 type of problems using Math. The way humans can learn to recognise patterns in numbers, images, speech & text similarly AI can also learn the same. These patterns help AI to solve puzzles, for example identifying a dog or cup cake or predicting a cyclone! Activity-3 Imagine a world where machines can learn, adapt, and even make decisions! That's the exciting world of Artificial Intelligence (AI), and guess what? Math is the secret sauce that makes it all possible! Here's why having a strong foundation in Maths is super important for AI: 1. Language of Numbers: AI deals with massive amounts of data. Think of all the information a self-driving car needs to process – traffic signals, pedestrian locations, and more. Maths provides the tools to understand, analyze, and use this data. It's like a special language that lets AI systems communicate and make sense of the world. 2. Building Intelligent Machines: At the heart of AI are algorithms – a set of instructions that tell a computer what to do. These algorithms are based on complex mathematical concepts like probability, statistics, and calculus. The stronger your Math skills, the better you can understand how these algorithms work and even design your own! 3. Training AI with Data: Remember all that data we mentioned? AI systems learn from it. Maths helps us clean, organize, and interpret this data. It's like preparing a delicious meal – you need the right ingredients (data) and the proper recipe (Maths) to create something amazing (AI)! 3 4. Making Predictions: Many AI applications involve making predictions. For example, a weather forecasting AI uses Maths to analyze weather patterns and predict future conditions. Strong Math skills help you understand how AI arrives at these predictions and how accurate they might be. Cool Examples: Facial Recognition Software: Uses Maths (like linear algebra) to recognize faces in images and videos. Recommendation Systems: Recommends movies or products based on your past preferences. Maths (like probability) helps analyze this data and make suggestions. Let's dive into the fascinating world of finding patterns in numbers and images, and how different areas of math come into play: 1.1 Finding Patterns in Numbers: Imagine you have a list of your monthly grocery bills. You can analyze them to find patterns and save money! Here's where math comes in: Statistics: Exploring Data We can calculate the average monthly bill to understand your typical spending. Standard deviation tells you how much your bills vary from the average. Are there months where you spend significantly more? Example – What is the middle value of the data? Which is the most common value in the data? 1.2 Finding Patterns in Images: Our world is full of visual information! Math helps us extract patterns from images: Linear Algebra: Images can be represented using matrices, which are like grids of numbers. Linear algebra helps us manipulate these matrices to identify patterns, like edges and shapes. Let's use an example! Imagine a checkerboard image. Each square on the board can be represented by a 1 (white) or 0 (black). By analyzing this matrix using linear algebra, we can find the straight lines formed by the squares of the same color! 1.3 More Mathematical Superpowers! Probability: Predicting different events We can use probability to predict future patterns in numeric data. For example, if your grocery bills have been steadily increasing, probability can help estimate how much they might be in the future. Calculus: Training and improving AI model This branch of math helps us find the most efficient or quickest way to change something based on patterns. In image processing, calculus can be used to optimize algorithms that detect patterns, making them faster and more accurate. Remember, this is just the tip of the iceberg! These mathematical tools are used extensively in AI and machine learning to find complex patterns in massive datasets, leading to amazing applications like: Facial recognition software: Uses patterns in facial features to identify people. 4 Medical diagnosis tools: Analyzes medical images to detect diseases. Hence, ▪ Math is the study of patterns ▪ AI is a way to recognize patterns in order to take decisions ▪ AI needs Math to study and recognize patterns in order to take decisions. Can you identify any pattern in the image ? 2.1 Statistics: Exploring Data Can you find out the total weight of your family members? ____________________________________________________ Can you find out the total number of students in your school? _____________________________________________________ Can you find out the maximum temperature in your city during the last month? ____________________________________________ Demystifying Statistics: Turning Numbers into Knowledge Statistics is a powerful tool that helps us understand the world around us using data. It's like having a superpower to see patterns and trends hidden within numbers. Here's a breakdown: What is Statistics? Imagine a giant pile of pebbles. Each pebble represents a piece of information, like student grades, weather data, or customer preferences. Statistics is the art of collecting these pebbles (data), organizing them, and making sense of them or drawing conclusions from data. It involves four key steps: 1. Collecting Data: This is where we gather information from various sources like surveys, experiments, or existing records. It's like picking up all those pebbles! 2. Exploring and Cleaning Data: Not all pebbles are created equal. Some might be chipped or broken (errors in data collection). We need to clean and organize the data to make it usable. 3. Analyzing Data: This is where the magic happens! We use statistical methods to identify patterns, trends, and relationships within the data. It's like sifting through the pebbles to see how they group together. 4. Drawing Conclusions: Based on the analysis, we can draw conclusions and make informed decisions. It's like using the insights from the pebbles to understand a bigger picture. How is Statistics Used in the Real World? Statistics has its fingerprints all over our daily lives! Here are some examples: 5  Predicting Sports Performance: Statistics can help analyze past game data to predict the chances of a team winning. Understanding Student Performance: By analyzing test scores, educators can identify areas where students might need extra help. Shaping Public Policy: Statistics from surveys can help governments understand public opinion and make informed decisions about healthcare, education, and other areas. Improving Business Decisions: Companies use statistics to analyze customer data, track sales trends, and make better marketing strategies. Activity – 4 Purpose: Uses of Statistics in real life. Write any two applications of Statistics in real life. ______________________________________________________________________________ ______________________________________________________________________________ Some more applications of Statistics Percentage of Different 1.1 Healthcare Diseases in a Population Explanation: Statistics in healthcare are used to track disease outbreaks, patient recovery rates, and OTHER 20% the effectiveness of new treatments. RESPIRATORY DISEASES 10% DIABETES 15% Examples: CANCER 25% Tracking the spread of diseases like COVID-19. HEART DISEASE 30% Analyzing patient recovery rates after a surgery. 0% 10% 20% 30% 40% 6 1.2 Disease prediction The Government uses statistics to understand which disease is affecting the population the most. ▪ This helps them in curing these diseases more effectively. Example - Government can analyze the areas where COVID cases are increasing, or where the vaccination drive needs to be improved. 1.3 Disaster Management ▪ Authorities use statistics to alert the citizens residing in places that might be affected by a natural disaster in near future. ▪ The disaster management teams use statistics to know about the population, and about the services and infrastructure present in the affected area. 1.4 Weather forecast ▪ Computers use statistics to forecast weather. ▪ They compare the weather conditions with the information about past seasons and conditions. Case Study: The 2004 Indian Ocean Tsunami Introduction The 2004 Indian Ocean tsunami was one of the deadliest natural disasters in recorded history. Triggered by a massive undersea earthquake off the coast of Sumatra, Indonesia, it resulted in widespread devastation across multiple countries. Statistical Data Related to the Event 1. Magnitude of Earthquake: o The earthquake that triggered the tsunami had a magnitude of 9.1-9.3. 2. Number of People Affected: o Approximately 230,000 to 280,000 people died. o Millions were displaced and affected by the tsunami. 3. Areas Most Impacted: o Countries affected included Indonesia, Thailand, Sri Lanka, India, Maldives, and several others. o The hardest-hit regions were the coastal areas of Aceh in Indonesia, Tamil Nadu in India, and various coastal towns in Sri Lanka and Thailand. 4. Speed of Emergency Response: o The international response was swift, with aid arriving from around the world within days. 7  o Local emergency responses varied significantly, with some areas receiving help more quickly than others. Activity for the students: Analyzing the Data 1. Collect Data: o Collect data from government reports, international organization publications, and reputable news articles. 2. Analyze the Data: o create graphs and charts to visualize the data. For example, you can create bar graphs showing the number of casualties in each country, pie charts representing the proportion of displaced people, and line graphs tracking the timeline of emergency response efforts. 3. Interpret the Data: o Write a report interpreting their findings. Questions to address include: ▪ Which countries were most severely affected? ▪ How did the speed of emergency response vary between different regions? ▪ What factors contributed to the differences in impact and response? Discussion: The Role of Statistical Analysis in Disaster Management 1. Understanding Impact: o Statistical analysis helps authorities understand the scale and scope of the disaster. For example, knowing the number of casualties and displaced individuals helps in planning relief efforts. 2. Resource Allocation: o By analyzing the areas most impacted, resources such as food, water, medical supplies, and rescue teams can be allocated more effectively. 3. Improving Response Times: o Data on the speed of emergency response can identify bottlenecks and areas for improvement. For instance, if certain regions received help more slowly, authorities can investigate and address the reasons behind the delays. 4. Future Preparedness: o Statistical analysis of past disasters can inform future preparedness plans. Lessons learned from the 2004 tsunami can help improve early warning systems, evacuation plans, and international coordination. Improvements for Future Events 1. Enhanced Early Warning Systems: o Invest in advanced technology to detect tsunamis and other natural disasters more quickly. o Ensure that warning messages reach the affected populations promptly. 2. Better Infrastructure: o Build and maintain infrastructure that can withstand natural disasters, such as tsunami barriers and earthquake-resistant buildings. 3. Community Training and Awareness: o Conduct regular training and drills for communities in disaster-prone areas to ensure they know how to respond in an emergency. 4. International Coordination: o Strengthen international cooperation for disaster response, ensuring that aid can be mobilized and distributed efficiently. 5. Data Collection and Sharing: o Improve methods for collecting and sharing data during and after a disaster to ensure accurate and timely information is available for decision-making. 8 Few more facts Kids watch around 1.5-3 hours of TV per day while being in childcare. 72% of teens often (or sometimes) check for messages or notifications as soon as they wake up, while roughly four-in-ten feel anxious when they do not have their cellphone with them. 77% of children don’t get enough physical exercise. Almost a quarter (23%) of children aged five to 16 believe that playing a computer game with friends is a form of exercise. 69% of all children experience one or more sleep-related problems at least a few nights a week. Only 54% of US children aged 3 to 5 years attend full-day preschool programs. At least 264 million children worldwide (about 12%) don’t go to school. Activity 5: Car Spotting and Tabulating Purpose: To implement the concept of data collection, analysis and interpretation. Activity Introduction: In this activity, you will engage in data collection and tabulation. Data collection plays a key role in Artificial Intelligence as it forms the basis of statistics and interpretation by AI. This activity will also require youth to answer a set of questions based on the recorded data. Activity Guidelines Data Collection Visit the following link or by scanning the QR code: https://www.youtube.com/watch?v=4A5L3x3TVuc&ab_channel=CarvingCanyons Fill the table while watching the video using tally. Cars Numbers of cars colour spotted Red Black White Data Analysis How many cars are spotted in total? ________________________________________________________________ Which colour has been spotted the maximum amount of time? ________________________________________________________________ Data Interpretation 9  What is the most common colour choice for the residents of this area? _______________________________________________________________ Answer hint: The colour observed the maximum number of times. _______________________________________________________________ 3.1 Probability Activity 6: To understand the possibility of occurrence of an event. Introduction to Probability: Fun with Predictions! Have you ever wondered how likely it is to rain tomorrow? Or how often you might get heads when flipping a coin? That's where probability comes in – it's the science of predicting how likely something is to happen! For example – When a coin is tossed, there are two possible results or outcomes: heads (H) or tails (T). The probability equation defines the likelihood of the happening of an event. It is the ratio of favorable outcomes to the total favorable outcomes. The probability formula can be expressed as, 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑜𝑓 𝐴 𝑃(𝐴) = 𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 Probability of an Event = Number of Favorable Outcomes / Total Number of Possible Outcomes We say that the probability of the coin landing H is ½ and the probability of the coin landing T is ½ When we talk about probability, we use a few terms that help us understand the chances for something to happen. 10 Classifying Events: The Probability Spectrum Probability isn't just about numbers. It also helps us categorize events based on how likely they are: Certain (Probability = 1): Events that will definitely happen. E.g., The sun will rise tomorrow (almost certainly!). Likely (Probability is high, but not certain): Events that have a good chance of happening. E.g., It might rain today based on the weather forecast. Unlikely (Probability is low): Events that are less likely to happen. E.g., Getting struck by lightning twice in your lifetime. Impossible (Probability = 0): Events that cannot happen. E.g., Finding a square watermelon in nature! Equal Probability: When all the outcomes in the sample space are equally likely. E.g., Flipping a fair coin (heads and tails have the same chance). If an event is certain or sure to happen, it will have a probability of 1. For example, the probability that it will rain in the state of West Bengal at least once in a specific year is 1. If an event will never happen or is impossible, it will have a probability of 0. For example, the probability that you can pick a red ball from a bag containing only blue balls is 0. 11 Let’s try to understand the concept of Probability using a relatable example. Consider a relatable scenario! You want to go to your best friend's birthday party next Saturday. Your parents decide to make a deal with you. Scenario 1 Scenario 2 12 Scenario 3 Scenario 4 Hope the terms impossible, unlikely, even, likely and certain are clearer now! Moving on, take a look at some applications of Probability in Real Life! PROBABILITY IN ACTION: MAKING EVERYDAY P REDICTIONS! Probability isn't just about problems in math class – it's a superpower that helps us navigate the real world! Here are some cool ways probability is used in our daily lives: 13 1. Cricket Champions: The Power of Averages Imagine your favorite cricket player. Probability helps us understand their batting average, which tells you how many runs they score on average before getting out. Let's say they scored 45 runs from boundaries in their last match (without running between the wickets). Based on probability, there's a chance they might score around 45% of their runs from boundaries in the next match too! This helps cricket analysts predict how a player might perform. 2. Weather Detectives: Predicting Rain or Shine Next time you check the weather forecast, you're using probability! Forecasters use complex data to calculate the probability of rain, snow, sunshine, etc. They might say, "There's a 70% chance of rain today between 4 PM and 6 PM." This means it's pretty likely to rain during that time. 3. Beating Traffic Jams: The Art of the Guesstimate Ever wonder if you'll get stuck in rush hour traffic? Probability comes to the rescue again! We use it to make educated guesses (probability predictions) about traffic based on factors like time of day, location, and weather. If it's usually bumper-to- bumper from 6 PM to 7:30 PM in your area, there's a high probability of getting stuck. Knowing this, you might choose to leave earlier or take a different route. 4. Gaming the System (Honestly!) Probability is even used in board games you love! Think about rolling dice in a board game. The probability of each number coming up is the same (assuming a fair die). This helps make the game fair and exciting! Let’s discuss 1. Does math play a crucial role in AI life cycle? _____________________________________________________________________ 2. What is statistics? _____________________________________________________________________ 3. What is probability? _____________________________________________________________________ 14 Terminology Statistics (Exploring Data) : Statistics is used for collecting, exploring, and analyzing the data. It also helps in drawing conclusions from data. Probability (predicting different events):It is a way to tell us how likely something is to happen. Calculus (training and improving AI model):: This branch of math helps us find the most efficient or quickest way to change something based on patterns. Linear Algebra (finding out unknown or missing values): Linear algebra is the branch of mathematics that studies vectors, matrices, and linear transformations. Patterns : Patterns are recognizable arrangements of numbers, shapes, colors, or even sounds. Key-learning 1. Math is essential for understanding AI models in depth. 2. Different math concepts used for AI are Statistics, Probability, Linear Algebra and Calculus. 3. Applications of math can be found in everyday life. Solved Exercise A. Multiple Choice Questions (MCQs) 1. What is the main reason why math is important in AI? a) To draw pretty graphs b) To understand and analyze data c) To make robots look cool d) To replace humans with machines (Answer: b) 2. What is NOT a recognizable pattern? a) Rainbow colors appearing in a specific order b) Random scribbles on a piece of paper c) The Fibonacci sequence in a sunflower d) The increasing size of planets in our solar system (Answer: b) 3. Which mathematical concept helps us describe patterns using formulas? a) Geometry b) Algebra c) Calculus d) Statistics (Answer: b) 4. AI can be used to _______ by recognizing patterns in data. a) solve puzzles b) write poems c) feel emotions d) all of the above (Answer: a) 15 5. What is the probability of getting heads when flipping a fair coin? a) 0 b) 0.5 c) 1 d) It depends on the coin (Answer: b) 6. A bag contains 3 red marbles, 2 blue marbles, and 1 green marble. What is the probability of picking a red marble? a) 1/2 b) 1/3 c) 2/5 d) 3/6 (Answer: b) 7. If a fair coin is flipped twice, what is the probability of getting heads both times? a) 1/4 b) 1/2 c) 3/4 d) 1/8 (Answer: a) 8. The average height of a group of students is 150 cm. What is the term used for this average value? a) Median b) Mode c) Mean d) Range (Answer: c) 9. In a survey, the most popular ice cream flavor was chocolate. What descriptive statistic is this? a) Median b) Mode c) Mean d) Range (Answer: b) 10. The equation y = 2x + 5 expresses a relationship between x and y. What is the slope of this equation? a) 2 b) 5 c) x d) y (Answer: a) 11. In the sequence 2, 4, 6, 8, what is the next number? a) 10 b) 12 c) 14 d) It cannot be determined (Answer: a) 12. The process of collecting, organizing, and interpreting data is part of which mathematical field? a) Probability b) Statistics c) Geometry d) Calculus (Answer: b) 13. AI recommendation systems use _______ to analyze your past preferences and suggest new items. a) addition b) subtraction 16  c) probability d) division (Answer: c) 14. Strong math skills are helpful for _______ when designing new AI algorithms. a) understanding existing algorithms b) creating more efficient algorithms c) both a and b d) neither a nor b (Answer: c) 15. Which of the following is NOT an application of probability in daily life? a) Predicting weather forecasts b) Winning the lottery c) Calculating traffic congestion d) Checking if a medicine is effective (Answer: b) B. Fill in the Blanks. 1. The ability to recognize patterns is a key skill in both _______ and AI. (Answer: math) 2. AI systems are designed to find patterns in data, like _______ , _______ , or _______. (Answer: numbers, images, speech) 3. Mathematicians use various tools to _______ patterns in data. (Answer: identify) 4. The _______ sequence is an example of a complex pattern found in nature. (Answer: Fibonacci) 5. Basic mathematical skills used in AI include _______ operations, _______ , and _______ analysis. (Answer: arithmetic, geometry, data) 6. The language of numbers allows AI systems to _______ and _______ the world around them. (Answer: communicate, understand) 7. _______ helps us clean and organize data used to train AI systems. (Answer: Math) 8. AI _______ predictions based on the analysis of data patterns. (Answer: makes) 9. Facial recognition software uses _______ to identify faces in images. (Answer: math) 10. _______ helps us understand the likelihood of events happening. (Answer: Probability) 11. The _______ outcome of an event is the one that actually happens. (Answer: actual) 12. A _______ event is one that has a 0% chance of happening. (Answer: impossible) C. Short Answer Questions 1. Briefly explain why recognizing patterns is important in math. Recognizing patterns helps us solve problems efficiently by finding underlying structures and making predictions. 2. Describe two ways mathematicians use math to analyze patterns. Mathematicians can use formulas to describe patterns and analyze how they change over time. They can also use statistical methods to find relationships between different variables within a pattern. 3. Give an example of how AI uses probability in real life. Self-driving cars use probability to predict the movements of pedestrians and vehicles, ensuring safe navigation. 17  4. Describe two ways to represent data visually. Data can be represented visually using histograms or bar charts to show the frequency of different values. Line graphs can be used to show trends or changes over time. 5. Give an example of how statistics is used in everyday life. Statistics are used in weather forecasting to analyze historical data and predict future weather patterns. D. Long answer type questions: 1. Describe the role of probability and statistics in training and evaluating AI models. How do these concepts contribute to the development of reliable AI systems? Answer: Probability and statistics play a crucial role in training and evaluating AI models. Here's how: Training: o Selecting Training Data: Statistical methods help us select representative and unbiased data samples for training the AI model. o Evaluating Learning: We use probability to calculate the likelihood of the model making accurate predictions based on the training data. Evaluation: o Performance Metrics: Statistical metrics like accuracy, precision, recall, and F1-score help us assess the model's performance and identify areas for improvement. o Error Analysis: Statistical analysis of errors helps us understand where the model struggles and allows for targeted adjustments. By leveraging probability and statistics, we can develop AI models that are more reliable, robust, and less prone to errors. These concepts allow us to quantify the model's performance, identify potential weaknesses, and ultimately build trustworthy AI systems. 2. Discuss the ethical considerations surrounding the use of AI in various fields like healthcare, & finance. How can we ensure ethical and responsible development and deployment of AI? Answer: The use of AI in various fields raises significant ethical concerns. Here are some examples: Healthcare: Bias in AI algorithms used for medical diagnosis or treatment recommendations can have life-altering consequences. Finance: AI-powered algorithmic trading can exacerbate market volatility and create unfair advantages for certain groups. Criminal Justice: Using AI for facial recognition or risk assessment in the criminal justice system can lead to inaccuracies and biased profiling. To ensure ethical and responsible development and deployment of AI, we need to consider: Transparency and Explainability: AI systems should be designed in a way that allows us to understand how they reach decisions, reducing the risk of bias. 18  Human Control and Oversight: Humans should remain in control of critical decision-making processes, even when using AI tools. Regulation and Standards: Developing ethical guidelines and regulations for AI development and deployment is crucial. By addressing these ethical concerns, we can leverage the power of AI for good and ensure it benefits everyone fairly and responsibly. Exercise A. Multiple Choice Questions (MCQs): 1. What is the main benefit of recognizing patterns in math and AI? a) Improves memorization skills b) Helps solve problems and make predictions c) Makes learning more fun d) Develops artistic abilities (Ans: b) 2. Which mathematical concept helps describe patterns using rules or formulas? a) Geometry b) Statistics c) Probability d) Algebra (Ans: d) 3. AI can learn patterns in what types of data? a) Numbers only b) Images only c) Text only d) All of the above (Ans: d) 4. AI excels at finding patterns in large amounts of data. What branch of mathematics is most helpful in describing these patterns? a) Algebra b) Calculus c) Geometry d) Statistics (Ans: d) 5. In the series 2, 4, 6, 8,..., what is the rule used to find the next number? a) Add 1 b) Add 2 c) Multiply by 2 d) Divide by 2 (Ans: b) 6. Which of the following is NOT a common application of statistics in AI? a) Identifying trends in customer behavior b) Recognizing objects in images c) Predicting the weather d) Solving systems of linear equations (Ans: d) 19  7. The process of collecting, organizing, and analyzing data to draw conclusions is called? a) Probability b) Statistics c) Calculus d) Algebra (Ans: b) 8. Which mathematical concept helps calculate the likelihood of an event happening? a) Geometry b) Statistics c) Probability d) Algebra (Ans: c) 9. AI algorithms are like recipes that tell a computer what to do. What mathematical concept is similar to a recipe with steps? a) Geometry b) Statistics c) Probability d) Algebra (Ans: d) 10. In the image processing field of AI, what mathematical concept helps analyze the arrangement of pixels in an image? a) Geometry b) Statistics c) Probability d) Algebra (Ans: a) 11. With one throw of a 6-sided die, what's the probability of getting an even number? a) 1/5 b) 2/5 c) 5/6 d) 1/2 12. Which of the following is an equation? a) 2x + 5 b) x + 2 = 4x c) x^2 + 2x d) 5 + 5x + 5x^2 13. What is the value of x? 10x-8=6x a) 8 b) 4 c) 2 d) 6 14. Which two are examples of descriptive statistics? a) Median and correlation. b) Mean and standard deviation. c) Mode and regression analysis. d) Variance and Hypothesis testing. 15. What is the probability of getting head when you toss a coin once? a) 0.75 b) 1 c) 0 d) 0.5 16. The median of the data: 155, 160, 145, 149, 150, 147, 152, 144, 148 is a) 149 b)150 c)147 d)144 B. Fill in the Blanks: 1. The ability to recognize arrangements of numbers, shapes, or colors is called __________. (Answer: Pattern) 2. AI uses _____________ to solve complex problems by finding patterns in data. (Answer: Math) 3. Data used to train AI systems needs to be _____________ and _____________ before it can be used effectively. (Answer: Cleaned, Organized) 4. A set of instructions that tell a computer what to do is called an ______________. (Answer: Algorithm) 20  5. When training an AI system, large amounts of ____________ are needed to help it learn patterns. (Answer: Data) C. Match the following: A B I) Probability a) exploring data ii) Calculus b) finding out unknown or missing values iii) Statistics c) predicting different events iv) Linear Algebra d) training and improving AI model. D. Short Answer Questions: 1. Explain two ways that math helps AI systems work. 2. Describe the role of statistics in the field of AI. 3. How does understanding patterns help us solve problems in math and AI? 4. Explain the relationship between Mathematics and Artificial Intelligence, providing justification for their interconnection. 5. Aman is confused, how probability theory is utilized in artificial intelligence, help Aman by providing two examples to illustrate its importance. 6. Define Certain events and likely events with examples 7. Write any two examples of Impossible and equal probability events D. Long Answer Questions: 1. Identify the likely, unlikely, impossible and equal probability events from the following a. Tossing a coin b. Rolling an 8 on a standard die c. Throwing ten 5’s in a row d. Drawing a card of any suite 2. Explain the concept of "The Language of Numbers" in the context of AI. 3. Discuss the importance of math skills for someone interested in pursuing a career in AI development. 4. Choose a real-world application of AI (e.g., facial recognition software, self-driving cars) and explain how math is used in its development and operation. E. Scenario Based Questions: 1. Imagine you're training an AI to identify different types of flowers in pictures. How would you use math to achieve this? 2. A scientist is studying weather patterns to predict the likelihood of a hurricane. How might they use statistics and probability in their research? F. Competency Based Questions: Age (in years) 10 12 14 15 16 Cases admitted (in a day) 5 7 9 22 11 21  1. Radhika collected the data of the age distribution of cases admitted during a day in a hospital. Find the average number of cases admitted in hospital. Also, draw a line graph to represent the data graphically. 2. You are tasked with designing a simple AI program that can identify basic shapes (circle, square, triangle) in images. How would you approach this problem using your understanding of math and patterns? 3. Imagine you're working on a team developing a new AI application for your school. What mathematical skills would be most valuable for you to contribute to the project? Explain your reasoning. Video-based Learning Interactive Worksheet (www.youtube.com/EdusoftKnowledgeverse) (playground.edusoft.co.in) Vc.0 22